Optimization Letters

, Volume 2, Issue 4, pp 445–454 | Cite as

The GLOBAL optimization method revisited

  • Tibor Csendes
  • László Pál
  • J. Oscar H. Sendín
  • Julio R. Banga
Original paper

Abstract

The multistart clustering global optimization method called GLOBAL has been introduced in the 1980s for bound constrained global optimization problems with black-box type objective function. Since then the technological environment has been changed much. The present paper describes shortly the revisions and updates made on the involved algorithms to utilize the novel technologies, and to improve its reliability. We discuss in detail the results of the numerical comparison with the old version and with C-GRASP, a continuous version of the GRASP method. According to these findings, the new version of GLOBAL is both more reliable and more efficient than the old one, and it compares favorably with C-GRASP too.

Keywords

Global optimization Direct methods Clustering Numerical tests 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balogh, J., Csendes, T., Stateva, R.P.: Application of a stochastic method to the solution of the phase stability problem: cubic equations of state. Fluid Phase Equilibria 212, 257–267 (2003)CrossRefGoogle Scholar
  2. 2.
    Balogh, J., Csendes, T., Rapcsák, T.: Some global optimization problems on Stiefel manifolds. J. Global Optim. 30, 91–101 (2004)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Banga, J.R., Moles, C.G., Alonso, A.A.: Global Optimization of Bioprocesses using Stochastic and Hybrid Methods. In: Floudas, C.A., Pardalos, P.M. (eds.) Frontiers in Global Optimization, pp. 45–70. Springer, Berlin (2003)Google Scholar
  4. 4.
    Bánhelyi, B., Csendes, T., Garay, B.M.: Optimization and the Miranda approach in detecting horseshoe-type chaos by computer. Int. J. Bifurcat. Chaos 17, 735–748 (2007)CrossRefMATHGoogle Scholar
  5. 5.
    Bánhelyi, B., Csendes, T., Garay, B.M.: A verified optimization technique to bound topological entropy rigorously. In: Proceedings of the SCAN-2006 Conference. IEEE 10, (2007)Google Scholar
  6. 6.
    Boender, C.G.E., Rinnooy Kan, A.H.G., Timmer, G.T., Stougie, L.: A stochastic method for global optimization. Math. Program. 22, 125–140 (1982)CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Csendes, T.: Nonlinear parameter estimation by global optimization—efficiency and reliability. Acta Cybern. 8, 361–370 (1988)MathSciNetMATHGoogle Scholar
  8. 8.
    Csendes, T., Bánhelyi, B., Hatvani, L.: Towards a computer-assisted proof for chaos in a forced damped pendulum equation. J. Comput. Appl. Math. 199, 378–383 (2007)CrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    Csendes, T., Garay, B.M., Bánhelyi, B.: A verified optimization technique to locate chaotic regions of Hénon systems. J. Global Optim. 35, 145–160 (2006)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Global Optim. 6, 109–133 (1995)CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic, New York (1984)Google Scholar
  12. 12.
    Hirsch, M.J., Meneses, C.N., Pardalos, P.M., Resende, M.G.C.: Global optimization by continuous GRASP. Optim. Lett. 1, 201–212 (2007)CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Hirsch, M.J., Pardalos, P.M., Resende, M.G.C.: Speeding up Continuous GRASP. Eur. J. Oper. Res. (2007) (submitted)Google Scholar
  14. 14.
    Horst, R., Pardalos, P.M. (eds): Handbook of Global Optimization. Kluwer, Dordrecht (1995)MATHGoogle Scholar
  15. 15.
    Järvi, T.: A random search optimizer with an application to a max-min problem. Publications of the Institute for Applied Mathematics, University of Turku, No. 3, 1973Google Scholar
  16. 16.
    Markót, M.Cs., Csendes, T.: A new verified optimization technique for the “packing circles in a unit square” problems. SIAM J. Optim. 16, 193–219 (2005)CrossRefMathSciNetMATHGoogle Scholar
  17. 17.
    Moles, C.G., Banga, J.R., Keller, K.: Solving nonconvex climate control problems: pitfalls and algorithm performances. Appl. Soft Computing 5, 35–44 (2004)CrossRefGoogle Scholar
  18. 18.
    Moles, C.G., Gutierrez, G., Alonso, A.A., Banga, J.R.: Integrated process design and control via global optimization—a wastewater treatment plant case study. Chem. Eng. Res. Des. 81, 507–517 (2003)CrossRefGoogle Scholar
  19. 19.
    Mongeau, M., Karsenty, H., Rouzé, V., Hiriart-Urruty, J.-B.: Comparison of public-domain software for black-box global optimization. Optim. Methods Softw. 13, 203–226 (2000)CrossRefMathSciNetMATHGoogle Scholar
  20. 20.
    Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic Global Optimization Methods, Part I: Clustering Methods. Math. Program. 39, 27–56 (1987)CrossRefMathSciNetMATHGoogle Scholar
  21. 21.
    Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic Global Optimization Methods, Part II: Multi Level Methods. Math. Program. 39, 57–78 (1987)CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Sendín, J.O.H., Banga, J.R., Csendes, T.: Extensions of a multistart clustering algorithm for constrained global optimization problems. Manuscript submitted for pubication. Available at http://www.inf.u-szeged.hu/~csendes/ReportGLOBALm.doc
  23. 23.
    Szabó, P.G., Markót, M.Cs., Csendes, T., Specht, E., Casado, L.G., García, I.: New Approaches to Circle Packing in a Square—With Program Codes. Springer, New York (2007)MATHGoogle Scholar
  24. 24.
    Tóth, B., Csendes, T.: Empirical investigation of the convergence speed of inclusion functions. Reliable Computing 11, 253–273 (2005)CrossRefMathSciNetMATHGoogle Scholar
  25. 25.
    Tóth, B., Fernández, J., Csendes, T.: Empirical convergence speed of inclusion functions for facility location problems. J. Comput. Appl. Math. 199, 384–389 (2007)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Tibor Csendes
    • 1
  • László Pál
    • 2
  • J. Oscar H. Sendín
    • 3
  • Julio R. Banga
    • 3
  1. 1.Institute of InformaticsUniversity of SzegedSzegedHungary
  2. 2.Faculty of Business and HumanitiesSapientia UniversityMiercurea-CiucRomania
  3. 3.Instituto de Investigaciones Marinas, IIM-CSICVigoSpain

Personalised recommendations